Reading List for Aspiring Mathematicians
May 8, 2021
My first college major was neuroscience. I learned about the beauty of mathematics by chance conversations, and eventually decided I deserved to give myself a chance to explore it. When I decided to switch my major to Honours Mathematics, I felt behind my peers who chose math as their major because they had been good at it growing up. After three years in graduate school, I have made my own contributions to mathematics and been invited to various places to present my work to the mathematical community. Although I still struggle with mathematics (as all mathematicians do), I no longer feel the same sense of insecurity that plagued me as an undergrad.
Here are a few of the readings I found useful, especially at the start of my mathematical journey. Also included are a few pieces of writing I found later on I wish I had the chance to read at a younger age. I hope this can be useful to the person who admires mathematicians but does not identify as a “math person”. I fully believe that, if you choose, you can become not only a “math person”, but a full-fledged mathematician.
Readings that helped me really understand math
Note: none of these were part of my undergraduate curriculum, but extra resources I found which helped me bridge the gap between what my program implicitly assumed I should already know and what I actually knew as an incoming student of mathematics.
Better Explained - this is the website which allowed me to truly understand how math was about concepts, not memorisation. It was especially enjoyable for me to re-learn some key concepts in trigonometry and functions and finally understand what they were about.
Gilbert Strang’s Calculus Book - I took Calculus I, II, and III without really understanding much. I had memorised how to do the problems and gotten disappointing grades in exchange. When I decided to major in math, I decided this wouldn’t do and took it upon myself to relearn the whole course sequence, focusing on the ideas rather than the computations.
A Book of Abstract Algebra by Charles Pinter - this was my first exposure to pure math and formal proofs. I found it illuminating to really attempt the exercises before checking the solutions. My approaches were embarrassingly wrong at first! It felt bad, but really taking the time to understand why I had been so wrong and why the solutions were right opened up the world of pure mathematics to me. To this day, coming up with a proof is the greatest joy of my life.
Readings that nourished my soul
A Mathematician’s Lament by Paul Lockart - a dissection of how mathematics is misrepresented in pre-college education.
Mathematics for Human Flourishing by Francis Su - who is mathematics for and what can we gain by learning mathematics?
On Proof and Progress in Mathematics by William Thurston - one of the greats of mathematics discusses what mathematical progress is.
Popular readings which propagate harmful ideas
A Mathematician’s Apology by GH Hardy
Peak by Anders Ericsson - a book dispelling the myth of born geniuses in various fields, including mathematics.
Piper H’s PhD thesis - Piper H, who graduated from Princeton (widely seen as the top school for mathematics), lays out her mathematical research in layman’s terms with great social commentary.
Warning: an apt description of most math environments.